The present disclosure concerns a method and a device for compensating the colorimetry of a projected image on a non-uniform projection surface.
An image is constituted by an array of elementary points called pixels. Each pixel in the image is typically represented by a triplet of numeric values (r, g, b) giving the intensity of the colour for the given pixel in a colour space, generally the colour space (R, G, B) of three base colours, namely red, green, blue. Other colour spaces may be used, for example, the colour space (Y,U,V) where the Y component represents the luminosity of the pixel, and (U, V) the chromatic components for coding the colour.
When such an image is projected using a video projector each projected pixel may not correspond exactly to the original pixel due to physical limitations of the video projector. Typically, the power of projection light is limited and the colour space available may not match exactly the original colour space. Moreover the luminosity decreases with the distance between the projector and the projection surface. The way the projector affects the source pixel to generate a projected pixel may be modelled as a transfer function.
When projecting the image on a projection surface, the perceived pixel will correspond to the projected pixel as reflected by the projection surface. The perceived pixel is therefore dependent on the albedo of the projections surface. The albedo corresponds to the “whiteness” of the surface, namely it is a reflection factor with a value between 0, corresponding to a perfectly black surface with no reflection at all, and 1 for a perfect reflection of a perfectly white surface. In actual projection condition, generally external light sources are present in addition to the projected image, meaning that the perceived pixel also depends on this additional light. We might summarize the relation between a given resulting pixel Pp in a projected image and the original pixel in the source image as follow:Pp=(P(Po)*Cd)*a+l  (1)
where Po is the original pixel, P(x) is the transfer function of the projector due to its physical limitations, Cd is an attenuation parameter due to the distance between the projector and the projection surface, a is the albedo of the projection surface and l is the contribution to the perceived pixel of the external light received on the projection surface at the pixel location. This equation may be simplified to integrate the attenuation parameter due to the distance and the projection surface albedo into a resulting albedo ar:Pp=P(Po)*ar+l  (2)
This equation would be true for the projection of a single pixel. When projecting a complete image of pixels, the light from the neighbour pixels interact with the projection of any particular pixels. A full model of the projection of an image may be summarized by the following equation:yu,v=Au,vi,jP(xi,j)+lu,v  (3)
Where yu,v is the two-dimension matrix representing the resulting image on the projection surface indexed by pixel coordinates (u, v). xi,j is the two-dimension matrix representing the source image being projected indexed by pixel coordinates (i, j). P(xi, j) is the two-dimension matrix representing the source image transformed by the projector, this is the actually projected image. Au,vi, j is a kernel representing the albedo. This kernel is a four dimensions matrix indexed by pixel coordinates (i, j) of the source image and pixel coordinates (u, v) of the resulting image. lu,v is a two dimensions matrix representing the contribution of external light on the resulting image indexed by the pixel coordinates (u, v).
It may be seen that the best projection conditions require a projection surface as close to a uniformly white surface with an actual albedo as close to 1 as possible used in a dark room with no external light.
It would be advantageous to get rid of the projection screen and be able to project on nearly any projection surface, even textured ones, like a wall in a room possibly integrating a textured wood door for example, and still get the best possible perceived projected image. It is also advantageous to consider that, in actual condition, the projection room is never perfectly dark and that the external light should be taken into account.
The problem is to improve the projection results of a video on a non-uniform projections surface in presence of external light.
A solution to this problem would be to determine the kernel Au,vi,j and the external light contribution lu,v then knowing the transfer function of the projector P, it would be possible to apply the inverse function of the model in equation (3) to the source image before projection in order to compensate the whole projection process and obtaining a resulting image on the projection surface that corresponds to the source image.
This theoretical solution suffers several drawbacks. The first challenge is the huge number of values to determine due to the size of the kernel. For example, using images in full HD resolution of 1920×1200, the kernel has about 5.3 1012 values to be determined. Another drawback lies in the physical capabilities of the projector. For example, compensating for a dark zone of the projection surface might require the projection of pixels with a light power exceeding the actual power of the projector.